Coherent Potential Approximation as a Voltage Probe

Abstract

Coherent potential approximation (CPA) has widely been used for studying
residual resistivity of bulk alloys and electrical conductivity in
inhomogeneous systems with structural disorder. Here we revisit the single-site
CPA within the Landauer-B\"uttiker approach applied to the electronic transport
in layered structures and show that this method can be interpreted in terms of
the B\"uttiker's voltage-probe model that has been developed for treating phase
breaking scattering in mesoscopic systems. We demonstrate that the on-site
vertex function which appears within the single-site CPA formalism plays a role
of the local chemical potential within the voltage-probe approach. This
interpretation allows the determination of the chemical potential profile
across a disordered conductor which is useful for analyzing results of
transport calculations within the CPA. We illustrate this method by providing
several examples. In particular, for layered systems with translational
periodicity in the plane of the layers we introduce the local resistivity and
calculate the interface resistance between disordered layers.